Transmission line with active networks



y 1947. K. s. JOHNSON TRANSMISSION LINE WITH ACTIVE NETWORKS Filed April 20, 1945 2 Sheets-Sheet 1.

Y v SECTION J SECTION 4 APPROX- EOl/IVALENT OF LINE WITH SHOOT/IL) DISTRIBUTED CONJTANTJ' V V SECTION 2 v SECTION I FIG. 2

SECTION I ACTIVE ACT I VE SE CT ION J 8 I NETWORK NE TWORK [CT 0 4 AC TIVE NETWORK ACTIVE SECTION 2 SECTION! NETWORK FIG. 4

smIIm INVENTOR K. s. JOHNSON ACTIVE NE TWORK v SECTION I ATTORNEY July 22, 1947.

' TRANSMISSION LINE WITH ACTIVE NETWORKS K. S. JOHNSON Filed April 20, 1943 2 Sheets-Sheet 2 A 5 RC R"C 5 l R"C 5f; 3 2 24 24 2 2 24 24 2 H r I n I I I -0-- c -c E i FIG 5 6 6 v I\ V J\ I v I I SECTION I ACTIVE NETWORK SECTION 2 T' u I Y Y LINE SECTION I LINE SECTION 2 (FIG-I) (FIG. I) 6 nm 5114c:

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rmqe; .& rwo sues 1E 1;!1 Two $7465 5 5 AMPLIFIER ua s AMPLIFIER INVENTOR I 1 K. S. JOHNSON ATTORNEY Patented July 22, 1947 TRANSMISSION LINE WITH ACTIVE NETWORKS Y Kenneth S. Johnson, South Orange, N. J., as-

signor to Bell Teleph porated, New York, N.

York

one Laboratories, Incor- Y., a corporation of New Application April 20, 1943, Serial No. 483,753

8 Claims.

The present invention relates to the use of networks containing negative impedance for improving the transmission characteristics of a telephone line or other type of line.

In accordance with the invention, networks of lumped impedances are inserted at intervals in a transmission line, these networks each presenting an impedance which is the negative of the impedance of a section of the line.

In attempting to provide a network that will annul the transmission loss of a section of line the problem arises of finding a physically realizable localized network of lumped impedances which will sufliciently accurately represent the characteristic of the line for all the frequencies of interest.

Taking as a representative case a telephone cable pair, I have devised networks which are closely equivalent in transmission characteristic to a section of line several miles long. These networks are physically realizable, and by the aid of vacuum tube amplifier circuits the negative of the impedance of such a network can be efiectively presented to the line in such a way as to largely annul or reduce the over-all attenuation- The invention will be more fully understood from the following detailed description, taken with the attached drawing in which:

Fig. l is an impedance diagram of an equivalent smooth line;

Fig. 2 shows the line of Fig. 1 equipped with negative impedance networks or active networks, according to the invention;

Fig. 3 is a further representation, in terms of lumped impedances, of a smooth line equipped with two-terminal active networks according to the invention;

Fig. 4 shows a similar line equipped with fourterminal active networks according to the invention;

Fig. 5 shows a different manner of representing the equivalent impedance of a line and of applying a negative impedance network according to the invention; and

Figs. 6 and 7 show how the negative of given positive impedances may be obtained and effectively applied to a line.

I have found that a non-loaded cable pair with smoothly distributed resistance and capacitance (neglecting inductance and leakage) can be very closely represented by pi sections made up as in Fig. 1 where each section represents a length of line whose resistance is R and capacitance is C.

If now, as indicated in Fig. 2, there be inserted between each two adjacent sections a shunt network made up of negative resistance of magnitude R/12 in series with negative capacitance of magnitude C, the resultant line has theoretically infinite shunt impedance and only the series resistance comprised of that of the sections in tandem. Such a structure will have theoretically no attenuation and maximum velocity of propagation. Actually, of course, zero attenuation could not be attained in any physical case. If attempt were made to connect negative resistance or negative impedance to its exact numerical positive equivalent, instability would result in practice. The rules for stability are well known and are given, for example, in Nyquist Patent 2,099,769, November 23, 1937. The rules for securing stability must be observed in setting up any practical'embodiment of this invention but within the limitations imposed by stability requirements the invention permits one to approach as closely as desired to the condition of making the negative impedance of an active network equal to the positive impedance which it faces and so, in the case of a transmission line, reducing the attenuation and delay both to neg ligibly low values.

The type of line equivalent given in Fig. 1 has been referred to as a second order pi network this being a type having but two elements in its shunt arm. A considerably closer equivalent is represented in the third order network shown in Fig. 3, section 1, in which inductance is introduced into the equivalent network representing the line. Taking as a representative example a 19-gauge cable pair, calculations show that this type of section gives a nearly precise equivalent for 5-mile lengths of cable for all frequencies up to 4 kilocycles, and gives very close equivalence up to l0-mile lengths and up to 4-kilocycle frequency. Consequently, by bridging a two-terminal active network across the circuit every 10 miles or so, having the negative impedance elements shown in Fig. 3, the total shunt impedance Y becomes nearly infinitely great, the attenuation of the complete circuit approaches zero and the velocity of propagation has maximum value. This is due to the fact, of course, that the impedance of the active network as employed is essentially the negative of the total shunt impedance of the line itself so that the two impedances in parallel give a nearly infinite resultant.

The type of active network shown in Fig. 3 is capable of giving nearly infinite shunt impedance but the series impedance still remains uncanceled. By employing four-terminal active networks of the type andin the manner shown in Fig. 4. not

network is the negative of the shunt impedance of the line section which it faces.

In Fig. the line is representedascomposed of T-seotions and the active networks are also'T- sections in which the impedances are the negatives of analogous impedances in the equivalent line sections. This type of network, also, is capable of giving nearly zero series impedance and nearly infinite shunt impedance. The approximation is not quite as close with the T-section as with the pi section shown in Figs. 3 and 4- but the approximation is very close in the case of the T-section up to 5 miles of 19-gauge cable and for .frequencies up to 4 kilocycles.

The manner in whichth'e' negative'impedances assumed in the previous figures canb'e obtained is illustrated by two examples-in Figs."6 and .7. Fig. 6 is applicable to the case shown in Fig.2, where a shunt comprising an element of impedance R/ 12 in series with an element of. im-

pedance -C is required. This isobtained by constructing a passive network of elementsR/ 12 and C in series with each other and placing them in theinput of an amplifier and also in shunt across the line in series with a feedback coupling from the output sideof the amplifier. This is in accordance with the teaching of Patents 1,779,382 .and 2,236,690 of 'R. C. Mathes which should'be consulted for 'furtherdisclosure of the exact circuitandmethod or operation. The phaserelation .around the amplifier and -feedback .paths mustbeproper and the degree of feedback adiusted to secure the desired effects.

Fig. '7 shows how .therequired negative 'impedancesforFig. 4 can be obtained. "The shunt branches of the active network are similar rtothat of Fig. 6 except that the negativeimpedance-derived from the amplifier is appliedacross the line in series with a positive inductance .of

value .Itwillibenote'd that this inductance isnotineluded .across the input terminals of the-am- .plifier. The series armis obtained by inserting .R and .is unstable when open-circuited vor connected across a positive'impedance ofgreater numerical magnitude than the negative impedance; and

that a series type negative impedance is unstable when short-circuited or'when connected in series with a positive impedance .of smaller numerical magnitudethan the negative impedance. It is, therefore, not practicalto exactly equate the negative impedance to the positive impedance in a circuit whether the negative impedance be of the series or shunt type since the circuit becomes practically unstable. The positive impedance must be at least slightly smaller in the shunt case and larger inlthe series case. The degree to which exaict equality can be approached with impunity depends upon the particular conditions governing any case. Usually a margin of stability is :left to take care of temporary or fortuitous changes in the system which might give rise to instability. The invention provides relationships whicharenearlyideal as disclosed and in the use 0f theinventionithe ideal relationships may be as closely approached as given conditions in any case permit. For convenience of definition certain of the'claims specify "substantial1y certain values or state that the values are relaxed sufliciently to insure circuit'stability. In view of the foregoing discussion of the question of stability, it is 'believedthat these expressions are clear and definite.

The references to certain sizes of conductor and spacing of active networks and the other numericalvalues areto be taken as illustrative and not as limiting the scope of the invention, which 'la'tter'is defined in the claims.

What is claimed is:

1. A transmission line of smoothly distributed constants having inserted therein at regularm- 'tervalsa succession of active networks dividing the'lineinto equal sections, each network including'at'least one branch shunted across the line "and'introducingacross the line a negative 1mpedancehaving as series components a negative resistance component and a negative capacitance component, said negative resistance component being numerically equal to fraction of the series resistance of each section of said line between adjacent active networks, each line section being :closely equivalent in transmission characteristics to .a given symmetrical .pi-network having its series arm substantially a lumpedresistance and having in-each of its two shunt arms a lumped resistance and a lumped capacitance in series, the product-of said resistance and said capacitance in each of said .shuntarms .beingnumerically substantially equal .to the product of said negative resistance component. and saidnegative capacitance component, and the numerical ratio of said capacitanceineach of said shunt arms to said capacitance in each of said branches being .half the number of said branches per active net- -work,,said.shunted networks rendering the line impedance substantially a resistance.

2. A wave transmission line with smoothly distributed resistance and capacitance-having impedance bridgedacross. said line at regular intervals, each bridging impedance having as series components a negative resistance component approachinga magnitude 3/12 and a negativecapacity component approaching .a magnitude C, where the line impedancebetween bridgingfpoints is substantially equivalent .to .a pi network having for its series arm a resistanceRand foreach shunt arm a resistance R/Gin series with a capacity 0/2, the degree ofapproachof the negative resistance and negative capacity values .-in the bridged impedancesto the values stated being relaxed suiiiciently. to insure. circuit stability.

3..A wave transmission line of smoothly distributed .constants having -impedances bridged across said. IineJat regular intervals,- each bridg- 'ingj impedance. comprising two portions in series, the first portion'having as series components a negative resistance component approaching a magnitude l t/l2, and a negative capacity component approaching a magnitude 0, and the other portion comprising a positive inductance approaching a magnitude Where the line impedance between bridging points is substantially equivalent to a, pi network having for its series arm a resistance R in series with an inductance and having for each of its shunt arms a resistance R/S, a capacity 0/2 and a negative inductance of magnitude in series with one another, the degree of approach of said elements to the values stated being relaxed sufiiciently to insure stability of the line against self-oscillation.

4. A wave transmission line of smoothly distributed constants having four-terminal active networks inserted therein at regular intervals, each such network being a pi network having for its series arm an impedance having two series components comprising a negative resistance component of magnitude substantially R and a negative component inductance of magnitude substantially and for each of its shunt arms an impedance of two series portions, the first portion having as series components a negative resistance component of magnitude substantially R/ 6, and a negative capacity component of magnitude substantially C/2, and the other portion comprising an inductance of magnitude substantially where the sections of line between the points of insertion of said active networks each has an impedance closely equivalent to that of a pi network having for its series arm a resistance R. in series with an inductance and for each of its shunt arms three elements in series comprising a resistance R/6, a capacity 0/2 and a negative inductance of magnitude each of the elements composing said active networks departing from the stated magnitude sufficiently to insure stability of the line against selfoscillation.

5. A wave transmission line of smoothly distributed constants having four-terminal active networks inserted therein at regular intervals, each such network being a T-network having for each of its two series arms two elements in series comprising a negative resistance of magnitude substantially R/2 and an inductance of magnitude substantially and for its shunt arm a resistance of magnitude substantially R/6 in series with a negative impedance having as series components a negative inductance component of magnitude substantially 48 and a negative capacity component of magnitude substantially C, where the sections of line between the points of insertion of said active networks each has an impedance closely equivalent to that of a T-network having for each of its two series arms a resistance 3/2 in series with a negative inductance of magnitude and for its shunt arm three elements in series comprising a capacity C, an inductance 48 and a negative resistance of magnitude R/6, each of the elements composing said active network departing from the stated magnitude suificiently to insure stability of the line against self-oscillation.

6. A transmission line of smoothly distributed constants having networks inserted at regular intervals therein, each having a shunt arm comprising as series impedances an inductance of small numerical value compared with the series inductance of the line between adjacent networks, and a negative impedance whose series components are: a negative resistance component and a negative capacitance component, said negative resistance component being numerically a fraction or" the value of the series resistance of the line between adjacent networks, said network substantially annulling the attenuation of said line.

7. A transmission line according to claim 6 in which said networks are four-terminal networks of pi-configuration, of which the series arm comprises a negative impedance having series components comprising a negative resistance component and a negative inductance component, and each shunt arm is a said shunt arm comprising an inductance in series with a negative impedance having as series components a, negative capacity component and a negative resistance component.

8. A transmission line of smoothly distributed constants divided into equal sections each closely equivalent in its transmission characteristics to a symmetrical pi-network having a series arm substantially lumped resistance and two shunt arms, each comprising identical lumped impedance, and means for reducing the line attenuation and rendering the lin impedance substantially a resistance, said means comprising a succession of active networks inserted in said line at regular intervals between said line sections, each of said active networks consisting of a shunt branch whose impedance is the negative of sub-- stantially one-half the impedance of a shunt arm of said equivalent pi-network.

KENNETH S. JOHNSON.

REFERENCES CITED The following references are of record in the file of this patent:

UNITED STATES PATENTS Number Name Date 2,137,696 Mouradian Nov. 22, 1938 1,955,681 Mouradian Apr. 17, 1934 1,687,253 Latour Oct. 9, 1928 

